Proposition 5

Tag 01BD, permanent. Cite it as [Bourbaki, Tag 01BD].

Lie Groups and Lie Algebras, chapter IX, § 3. Compact forms of complex semi-simple Lie algebras

Every compact simple real Lie algebra of type $B_n,n\geq 1$ (resp. of type $D_n,n\geq 3$ ) is isomorphic to $\mathfrak{o}(2n+ 1,\mathbf{R})$ (resp. $\mathfrak{o}(2n,\mathbf{R})$ ).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Proposition 6, § 3

Cites

Nothing.